Apart from the mutable keyword, can't these be implemented as a clang diagnostic plugin? Then it can be used to enforce a stricter style guide. As another commenter pointed, mutable will be probably of limited use anyway.
However, C++ is a huge language and if there's a way to enforce safety by using only a subset of the language + tooling to help you do that, your improvements could be adopted piecemeal by teams looking to level up their codebase a bit.
Many languages have a way to opt in to e.g. strict type checking on a per-file basis. It would be really cool to see these improvements implemented in such a way that existing codebases could gradually adopt them.